Chronon Quantum Gravity: Emergent Spacetime from a Dynamical Temporal Field

Unifying quantum mechanics and general relativity remains one of the most profound challenges in theoretical physics. While quantum theory is built upon probabilistic dynamics in a fixed spacetime background, general relativity treats spacetime itself as a dynamical entity governed by the Einstein field equations. This tension becomes especially acute in regimes of strong curvature, such as black hole interiors and the early universe, where a consistent theory of quantum gravity is indispensable. A major conceptual barrier to such a unification is the treatment of time. In standard quantum theory, time is an external parameter, an absolute classical variable that orchestrates the evolution of quantum states. In contrast, general relativity regards time as a coordinate subject to diffeomorphism invariance, with no privileged role. The resulting tension gives rise to the so-called problem of time, which plagues canonical quantizations of gravity such as the Wheeler–DeWitt framework. These approaches often yield a “frozen formalism,” in which the wavefunctional of the universe appears static, challenging any straightforward interpretation of dynamical evolution. Chronon Quantum Gravity (CQG) offers a radical departure from these conventions. It is grounded in Chronon Field Theory (CFT) , which postulates that time is not merely a coordinate or external parameter but a physical, dynamical field—a smooth, unit-norm, future-directed timelike vector field Φμ(x) defined on a Lorentzian manifold. This field, termed the Chronon field, encodes local temporal flow and induces a preferred foliation of spacetime into spatial hypersurfaces orthogonal to Φμ. The orientation and topological structure of this field define causal cones, temporal ordering, and the global arrow of time. Crucially, all observed physical phenomena—including matter fields, gravitational interactions, and quantum behavior—are understood as emergent from the evolution and topology of Φμ. Chronon Quantum Gravity (CQG) is formulated as a background-independent, quantizable, and topologically regularized theory of gravity. Unlike approaches that attempt to quantize geometry directly, CQG treats geometry as emergent from the quantum dynamics of temporal flow. The theory is founded on a constrained vector field Lagrangian with intrinsic topological structure, permitting a well-defined quantization procedure that avoids the pathologies of non-renormalizability and background dependence. In this paper, we develop the theoretical foundations of CQG and demonstrate its capacity to address key challenges in quantum gravity. We construct a Chronon-adapted Wheeler–DeWitt equation that resolves the frozen time problem. We show that General Relativity emerges in the classical limit as a large-scale manifestation of Chronon alignment. We propose a topological definition of black hole entropy derived from winding numbers of Φμ and present a concrete numerical simulation scheme to study the emergence of spacetime and entropy from a disordered temporal substrate. In doing so, CQG offers a coherent, predictive, and empirically accessible framework that reinterprets spacetime, matter, and quantum evolution as manifestations of a deeper temporal ontology.